Question

Four years ago the sum of the ages of mother and daughter was 29 years and four years hence mother's age will be four times that of her daughter.Find the present ages of mother and her daughter

Answer 1

present age of mother and daughter is X and Y
four years ago

(x-4)+(y-4)=29
x-4+y-4=29
X+y=37..........(1)
four years hence
X+4=4(y+4)
x-4=4y+16
x-4y=12.......(2)

simplify (1) &(2)
X+y=37
x-4y=-12
= 5y=25
y=5
X+5=37
X=32

Answer 2

let mothers age four years ago be x-4
let daughters present age be y-4 
ATQ
x-4+y-4=29
x+y-8=29
x+y=37   ------ eq1

mothers age four years hence =x+4
daughters age 4 years hence=y+4

ATQ
x+4=4(y+4)
x+4=4y+16
x-4y=12   ---eq2

solving 1 and 2

x+y=37
x-4y=12
-  +    -
______
    5y=25
        y=25 divided by 5
y=5

substitute y in eq 1

x +5=37
x=37-5 
=32